' /ANL-77-52ANL-77-52

APPLICATION OF THE

PULSED-NEUTRON-ACTIVATION TECHNIQUE

FOR FLOW MEASUREMENT AT EBR-

by

C. C. Price, J. I. Sackett, R. N. Curran,

C. L. Livengood, P. Kehler, and G. A. Forster

APPLIED TECHNOLOGY

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-

TABLE OF CONTENTS

ABSTRACT......... .....................................

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

II. ANALY'1IC MODELING . . . . . . . . . . . . . . . . . . . . . . . . . .

A. Review of Models. . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Activity-ratio Technique. . .................. .2. Pulsed-neutron-activation Technique. . . . . . . . . . . . .

B. PNA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

C. Measurement Uncertainty . . . . . . . . . . . . . . . . . . . . . .

I1. EXPERIMENT DESCRIPTION . . . . . . . . . . . . . . . . . . . . . .

A. Eqi

1.2.3.

B. Ge(

1.2.3.

C. Tec

iipment....... ............................

Instrumentation . . . . . . . . . . . . . . . . . . . . ..Shielding... . . .. ..........................Shielding and Collimation for Gamma Detector .

)metry . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Mockup Test . . . . . . . . . . . . . . . . . . . . . . . .

Measurement of Flow through Evaporator Downc

Measurement of Secondary-sodium Flow . . . .

st Conditions . . . . . . . . . . . . . . . . . . . . . . . .

o e r s

IV. DATA..... . ...............*.0.0 . . . . . . .

A. Mockup Test . . . . . . . . . . . . . . . . . . . . . . . . . . .

B. Evaporator-downcomer Flow . . . . . . . . . . . . . . . .

C. Secondarysodium Flow. .......... . 0............. .

V. DATA ANALYSIS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A. Mockup Test . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B. Evaporator-downcomer Flow . . . . . . . . . . . . . . . . . . . . .

C. Secondary-sodium Flow................ . . ......

Page

9

9

10

10

10

11

12

19

27

.f7

27

2728

28

28

3131

36

. . .37

37

37

38

41

41

42

43

3

4

TABLE OF CONTENTS

Page

VI. DISCUSSION ... ....................... . . . . . . . . . 49

A. M ockup Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

B. Evaporator-downcomer Flow.............................49

C. Secondary-sodium Flow. . . . . . . . . . . . . . . . . . . . . . . . . . 49

VII. CONCLUSIONS AND RECOMMENDATIONS . . . . . . . . . . . . . . . 50

A. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

B. Recommendations.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

APPENDIXES

A. Count HisLory for Multiscaler . . . . . . . . . . . . . . . . . . . . . . 52

B. Procedure for Data Reduction . . . . . . . . . . . . . . . . . . . . . . 61

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

REFERENCES...................................... 66

5

LIST OF FIGURES

No. Title Page

1. Block Diagram of Pulsed-neutron Flow-measuring System. . . . . 12

2. Model Used to Estimate Detection Asymmetry due to Self -

abs rption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3. Block Diagram of PNA Instrumentation . . . . . . . . . . . . . . . . . 27

4. Diagram of Shield for Portable Neutron Collimator. . . . . . . . . . 28

5. Portable Neutron Collimator (Front View). . . . . . . . . . . . . . . . 29

6. Geometry of Neutron and Gamma Collimators and Shields . . . . . 29

7. Fixed Neutron-collimator Shield Mounted against Secondary-

sodium Pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

8. Gamma Shield and Dolly. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

9. Schematic Diagram of PNA Mockup Test in Water System . . . . . 31

10. Location of Neutron Generator and Gamma Detector for PNA

Measurement of Flow through Evaporator Downcomer. . . . . . . . 32

11. Schematic Diagram of EBR-II Secondary-sodium Flow Path endSteam-generation System. . . . . . . . . . . . . . . . . . . . . . . . . . . 33

12. Radial Geometry of Neutron Source and Gamma Detector with

Respect to Pipe Carrying Secondary-sodium Coolant. . . . . . . . . 33

13. Location of Neutron-output Monitor and Neutron-generator

Shield for Measurement of Secondary-sodium Flow. . . . . . . . . . 34

14. Gamma Detector and Shield Shown Located against Secondary-

sodium Pipe for PNA Measurement of Flow. . . . . . . . . . . . . . . 35

15. Count History for Mockup Test at a Nominal Flow Velocity

of0.6m /s. . .. . . . . . . . . . . .. . . ... ... . . . . . . . .. . . ... 37

16. Count History for Measurement of Flow through Downcomer ofEvaporator EV-708 at 30. MWt............................... 38

17. Count History for Measurement of Secondary-sodium Flow with

Flow Level at Nominal 90% of Full Flow . . . . . . . . . . . . . . . . 40

18. Flows Indicated by EM and Foster Flowmeters Plotted asFunctions of Flow Measured by PNA . . . . . . . . . . . . . . . . . . . 46

19. Divergence between Flows Indicated by PNA and EM and FosterFlowmeters, with PNA Assumed to Measure Flow Abso1.utely . . 47

B.1. Idealized Count History for PNA Measurement, Showing Break

Points. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6

LIST OF TABLES

No. Title

I. Test Conditions for Measurement of Flow through Evaporator

Downcom ers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

II. Experimental Parameters for Measurement of Secondary-

sodium Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

III. Secondary-system Volumetric Flow Rates as Measured by theEM and Foster Flowmeters................... . . . . . . ..

IV. Flow Velocities in Mockup Test . . . . . . . . . . . . . . . . . . . . . .

V. Constants of Fitted Data from Downcomer-flow Measurement

VI. Flow Velocities in Evaporator Downcomers . . . . . . . . . . . . . .

VII. PNA-measured Flow Velocity for Secondary Sodium System . .

VIII. Comparison of Secondary-system Volumetric Flow Rates

as Measured by Electromagnetic and Foster Flowmeters and

PNA: Sodium at 577 K. .................... . . . . . .

IX. Comparison of Values of t and 1/(I/t) for Measurements of

Secondary- sodium Flow. . . . . . . . . . ...............

A.l. Count History fo. PNA Mockup Test: Nominal Flow Level

0.6 m/s, Multiscai.er Channel Width 25 ms . . . . . . . . . . . . . . .

A.2. Count History for PNA Measurement of Flow through Down-comer of Evaporator EV-708: Nominal Flow Level at 30 MWt,Multiscaler Channel Width 25 ms . . . . . . . . . . . . . .

A. 3. Count History or PNA Measurement of Sodium Flow:Flow Level 10%, Multiscaler Channel Width 50 ms . . .

A.4. Count History for PNA Measurement of Sodium Flow:

Flow Level 20%, Multiscaler Channel Width 25 ms . . .

A. 5. Count History for PNA Measurement of Sodium Flow:Flow Level 40%, Multiscaler Channel Width 10 ms. . .

A.6. Count History for PNA Measurement of Sodium Flow:

Flow Level 60%, Multiscaler Channel Width 10 ms . . .

A.7. Count History for PNA Measurement of Sodium Flow:

Flow Level 80%, Multiscaler Channel Width 5 ms. . .

A.8. Count History for PNA Measurement of Sodium Flow:

Flow Level 90%, Multiscaler Channel Width 5 ms... .

A.9. Count History for PNA Measurement of Sodium Flow:Flow Level 95%, Multiscaler Channel Width 5 ms. . . .

Nominal

Nominal

Nominal

Nominal

Nominal

Nominal

Nominal

Page

39

39

41

41

44

44

45

45

50

52

53

54

55

56

57

58

59

60

LIST OF TABLES

No. Title Page

B. 1. Sample of Data Reduction Using Count History fromTable A.8 with NG = 10. ............................. .. ... 63

B.Z. Constants Determined from Fitting Data Obtained fromSeconda--y-sodium System at 90% Flow. .... 0....... ........... 64

B.3. Results from Using Each Fitted Form of Table B.2 forBackground Correction . . . . . . . . . . . . . . . . . . . . . . . . . ... 64

9

APPLICATION OF THEPULSED-NEUTRON-ACTIVATION TECHNIQUE

FOR FLOW MEASUREMENT AT EBR-II

by

C. C. Price, J. I. Sackett, R. N. Curran, C. L. Livengood,

P. Kehler, and G. A. Forster

ABSTRACT

This report describes the pulsed-neutron-activation

(PNA) flow-measuring technique as applied to in situ fluid-flow

measurements at EBR-II. Analytic relationships are derived

for modeling the process and estimating the uncertainty in the

measurement. Results from measurements of both water flow

and secondary-sodium flow are presented. Results from PNA

measurements on the water side of the EBR-Il steam system

have led to better definition of plant parameters. Results from

sodium-flow measurements are used to provide a correlation

for in situ calibration of the electromagnetic sodium flow-

meter in the secondary system.

1. INTRODUCTION

As the mission of the Experimental Breeder Re ctur Ii (EBR-I) hasevolved from demonstrating the practicality of the breeding concept and a cum-patible fuel cycle to serving as an irradiation facility and tet reactor for theU. S. LMFBR program;, it has been nece'sary to , ha racterize systems forwhich the original mission provided inadequate or no instrumentation. In ad-dition, it has been necessary to verify the calibration of sensors for certainsodium and water flows in the EBR-Ul r'cundary-sodiium and steam systems.To meet these requirements, a neutron-activation technique has been suc~css-fully used to measure both sodium and water flow rates in thewv systems.

Neutron-activation methods for measuring flow are basic ally extensionsof radioisotope-tracer techniques that have been in use for some years."

These techniques are, in turn, improvements on chemical and dye tracer tech.niques. The improvements that the neutron-activation methods offer over theraiioisotope-tracer methods a re (1) simplic ity of introduri n ; activated nucleiinto the moving material. () no penetration of the system piping. (3) ns 4is-.turbanee of the fluid flow p ttern, because+ the activated ni' ar formedin situ, and (4) no hand'un of radioeative tracer trials.

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13. PNA Model

The instrument configuration used for the PNA measurement is shown

in Fig. 1. Briefly, the neutron generator (source) is positioned at a selected

location on the fluid-bearing pipe, and a gamma scintillation detector is located

a suitable distance downstream. After a pulse of neutrons from the generator,

the signals from the scintillation detector, monitoring gamma rays from pas-

sage of the activated nuclei, are amplified and then passed through a single-

channel pulse-height analyzer. The analyzer has lower- and upper-level

energy discrimination, which can be set to allow passage of only the selected

gamma-ray energy. Those gamma signal pulses passed by the analyzer are

routed to the multiscaler. where they are correlated to provide a count-rate

time history. A common control initiating the neutron pulse and simultaneously

starting the multisraler may be repetitively operated to accumulate counts from

several neutron pulses in the multiscaler channels. However, a delay period

between neutron-injection pulses must be used to allow the activated fluid to

completely pass the detector and the multiscaler to complete its cycle.

) iok 'ION _4

PULSEDNEUIRON DE ECTGRSOURCE

AMPLIFIER

CONTROL

SINGLE-CHANNELANALYZER

CONTROL MULTI-

PULSES SCALER

Fig. 1. Block Diagram of Pulsed-neutron Flow-measuringSystem. ANL Neg. No. 103-T5875.

To determine the fluid velocity from the measured data, we must deter-

mine the transit time between the injection and detection sites. To do this, we

turn to analytic relationships developed and tested by Sir Geoffrey Taylor,4' 5

which describe the transport of a tracer material in a fluid flowing in a straight

pipe. Taylor showed both theoretically and experimentally that, in a pipe, the

center of diffusion for a tracer initially on a plane perpendicular to the flow

moves at the mean velocity of the flow (i.e., x = Vt). He showed that this was

the case in round, straight pipes for both laminar4 and turbulent flow.'

13

In his analytic work, Taylor developed the transport model for a tracer

material that is instantaneously and uniformly injected on a plane across the

pipe. He found that, as this tracer material moves downstream in the pipe,

it is acted on by fluid molecular and velocity effects that cause it to develop

a concentration distribution havig a Gaussian spatial shape along the axis of

the pipe. For laminar flow, Taylor found that molecular diffusion is the domi-

nant mechanism leading to development of the Gaussian spatial shape, but thatmacroscopic turbulent effects related to the Reynolds number dominate in for-

mation of the Gaussian distribution for turbulent flow. He developed effective

diffusion coefficients for both cases.

Taylor's most important finding in regard to flow measurement by PNA

is that the center of the concentration distribution moves with the mean fluid

velocity. As will be shown later, this does not imply that the mean transient

time determined from the PNA measurement is the properly weighted transportfor use in determining 1.he mean fluid velocity. It is not. However, Taylor'sfinding does imply that the mean fluid velocity is uniquely determinable from

the PNA measurement.

As a starting point, we take the following relationship developed by

Taylor (Eq. 6.1 of Ref. 5) for dispersion of a fluid tracer material in a long

straight pipe:

C(x, t) = At~'z exp[ -(x Kt], (5)

where

C(x, t) concentration at a time t and distance x downstream of theinjection site,

A = constant dependent on the initial amount of material injectedon a plane perpendicular to the pipe axis at x = 0,

t = time after injection,

x = distance downstream of the injection site,

V = mean fluid velocity,

and

K = effective diffusion coefficient.

This form is valid for both laminar and turbulent flow. The supporting rela-tionships are:

Laminar Flow

K-9dzVz-92D' (6

14

where

d = pipe diameter

and

D = molecular diffusion coefficient.

Fully Developed Turbulent Flow

K = 5.05 dVV

and

/= ,

where

T = turbulent friction stress

and

p = fluid density.

For fully developed turbulent flow in smooth pipes, the ratio v*/V de-

pends only on the fluid Reynolds number, Re, and can be expressed as

where

y~/Z = -0.40 + 4.00 log1 0 Re + 2.00 log10 y.

(9)

(10)

For rough pipes, one must return to the definition of v* and obtain thefriction stress

or _ d dpTo =(LI)4dx

for that pipe.

When a radioactive tracer is used, the initial amount of tracer materialwill deplete by decay. To accommodate this effect, Eq. 5 is modified as follows:

-,/z (x - Vt)IA(x, t) = Aot i"exp - 4t - At ,t2

(7)

(8)

= ,_

15

where

Ao = a constant related to the initial activity injected

and

X = decay constant of the activated isotope.

Examination of Eq. 12 shows the following characteristics:

I. At a given time t = T, the activity distribution is a Gaussian dis-

tribution in space that moves at the mean velocity of the fluid, V.

2. When measurements are made at a fixed point a distance L down-

stream from the injection site, the observed distribution in time is neither

Gaussian nor symmetrical.

If one measures the spatial distribution at time T and locates the cen-

troid, maximum, or mean of the Gaussian distribution at x = X, then V = X/T

is the mean velocity. The situation is not so clear for the case where the mea-

surement is made by a single detector fixed at a distance L downstream. Wecan fit the time-distribution relationship A(L, t) of Eq. 2 to the data to obtainthe mean fluid velocity, V, or we can seek the proper weighting term to applyto the distribution. Following this latter option, we derived the following mo-ments from the activity distribution (Eq. 12):

tA(L,t)dtt = .(l3)

f A(L, t)dt

and

f A(L. t)dtt/t= t (14)

JA(Lt)dt

Following the above procedure and making use of the relationship VL/T, we find the resultant relationships to be

-L KT/1

16

arma

1/t= l+ 4KzIJ- (16)L T

Examination of the above relationships shows that each is biased and

also that forms involving tZ or its reciprocal will exhibit bias. However, con-sider a method by which the PNA data can be processed to eliminate the bias.

kfter removal of background (if any) from the count distribution, the count dis-

tribution can be multiplied by the factor eXt. This effectively reduces to zerothe contribution of X to the processed data. Then the preceding equationsbecome

t + T (17)

and

1/t = -. (18)

The proper weighting relationship for the PNA flow-measuring technique thenis l/t after the distribution has been corrected for decay.

In reviewing the preceding derivation, we see that the term e-'t couldhave been removed from the distribution relationship (Eq. IZ) by requiring thatthe distribution be corrected for radioactive decay prior to taking moments;however, it is instructive to consider the results of moments from the mea-sured distribution.

Within the constraints of Taylor's development, the above relationshipsare valid for "oth laminar and turbulent flows in pipes. These constrai ts aresurmnmarized below.

Laminar Flow

I. The changes in concentration of the tracer material due to transportalong the pipe take place in a ti e that is short compared tr mo seculardiffusion.

Z. The time necessary for appreciable effects to appear due to Cn.vective transport is long compared with the "decay time" during which radialvariations of the concwntration equilibrate. This csndtimn is expressed quanti-tatively as

IL a .1 1oftV.14

17

Turbulent Flow

1. The changes in concentration of the tracer material due to trans-

port along the pipe take place in a time that is short compared to turbulent

fluid diffusion.

2. The time constant for radial mixing in the pipe is short compared

to the transport time between the injection and detection sites.

When the effective diffusion coefficient for laminar flow (Eq. 6) is sub-

stituted into Eq. 17, the resultant time estimator

t = T + --D laminarr flow) (19)

will always be biased by the amount d/96D, and the bias is independent oftime or axial distance.

When the effective diffusion coefficient for turbulent flow (Eq. 7) is sub-stituted in Eq. 17, the resultant time estimator is

d O1 + 1)0.1 T. (10)

For this case, the estimator bias is dependent on the axial position of the de-tector, L, and the ratio v,/V. which is a function of Reynolds number. By useof Eqs. 12 and 13, it can be shown that the ratio v ' is a weak function of theReynolds number, varying fron. -0.07 at Re = 4000 to -0.03 at Rft= 10'. Asa result of this, the biasing part of Eq. 20. 10.1 (d. L) (viV) will be less thand/L. With this result, it is evident that for turbulent flow the error induced byuse of t as the estimator will be less than djL and that as d/L approaches 0,I approaches T. However, since it is as easy to obtain ltot as to obtain i, thereis little need to be concerned with the usr of a biased estimator, as the correctweighting function has been shown to be It.

The preceding analysis has considered snly the case for injection of atracer material on an infinitely thin plane. However, any injection distributioncan be represented as a sunr of thin planes. and sinca at a point sufficiently fardownstream each plane reduces to a Gaussian distribution along the pipe axis,one can consider the resultant distribution as a su of Gaussian distributions.In accord with the Central Limit Theorem,' this svm of Gaussian distribctnswill itself be a Gaussian distribution. Obviously an axially symmetric trscerinjection will assume the Gaussian shape more quickly (e.g.. in a shorter dis-tanet) than a nonsymmetrir injection. The symmetric injection also has anadvantage in that Its geoetric emner is #ceurately known. The idni1 injectionwould be one for which the activity injection is Gaussian.

18

In the PNA measurement, the data are normally collecteu by a multi-

channel analyzer with all channels set at a constant width, At. As a result, the

working relationship for determination of the mean reciprocal time, 1/t, is

I

- C(ti)cxp(Ati)1/t = 1, (Z1)

C(ti)exp(X ti)i=I

where

C(ti) = number of counts at time ti (for a multiscaler, i is the channelnumber),

I = the nutr;" r of time periods or channels used,

and the term exp(Ati) is applied to correct for decay between the activation anddetection times. The above relationship is the finite form of Eq. ' when thefollowing conditions are met:

Vtt < w (Lt)

and

w << 4KX'V. (23)

where

w the width of the detector window.

For these conditions, C(t 1) k A( i) t.

The mean fow velocity them Is

V u LIjt). (24)

Further, for ease of notation. define the mean rciproal tIme (Mitt) as

a ai.;(ZS)

then.,

V ELe. ()(24 )

19

Thus, the average flow velocity may be obtained by weighting the inverse

of the individual transit times over the normalized time distribution of the re-

corded count history.

C. Measurement Uncertainty

The uncertainty in the measurement is estimated by using the relation-ship for normally distributed error (Eq. 27 below). The minir Al requirementsthat the uncertainties of the parameters be normally distributed and that theuncertainties of independent parameters be independent is in general met orclosely approximated by the experiment parameters. This relationship is de-fined as

Nii

where

r = the uncertainty in the qi parameter, nominally the standarddeviation,

the standard deviation of the vetoity,

and

q = the parameter variable.

The other parameters are a* defintd4 arier.

Substituting the veltcity relationship (Eq. 24) into Eq. 27. performingthe indicated operations. and normalizing to the mean veocity, we obtain, forthe estimated fractionat variance in the flow velocity.

cV L'

-(a --)+ -- .*(NW

The uncertainty in L. L 6 dependent on the procisiun with wich Lcan be measured. Obviously the distance L an be inreased to reduce j;.to an acceptable agnitude. Because of finite col nation of the neutrons.however, there is a spatial dispersion of the activated nocle about L that isa function of a. Consequently, not all arrival times are for particles travelingexactly the distance L. To observe this ettvct, we expand the term # tlt) inthe Taylor series to obtain

"dip ) (9

20

If we define the spatial distribution-density function for the activated nu-clei as p(z), the mean transit time averaged over the spatial distributionbecomes

)n Lp(x)dr.

t .) n= o

By interchanging the order of integration and summation and expanding theseries as follows

F-f- [' - ---- pt)d + -- ()p(j)da

C f*

*I (j~p(xt)dz e p~~d - ..

we can find the movements of the spatially averaed v*ale of 1?&()). Only theeven movements have ;sutero values, the steind ot whuh .s reconixrd as thevariang x. By treating at thr s*eond eomnt, we find the uncertaintyusing t.t(a) to be

.... a --... (z..t(a* W()

or

Thwa the variac*. (al ih ). wto iht d vaih* .4 a ta d the iiatil atialaiatribmU o *4 ac ivatd s ev 1i ( #t'. This aw is ih.* adef 11 th eeertaity sitrknati ti permit a Uti #t 4 . a*4 n l#I?6$ sat a1*s1di-tribti f e ativatd weeai.

Th *minr lmres** d+ t . #fi hImti i#* 6 th* uw#rta ty *seisaiela clea ly evident #r m E. # a a 64 damm t hs4 ye fella a m .

as th*at 0- tivad )a ris 4r sio4 #y d a s 4410". 4h# 44. ""au4l *4 th pE 0.*0% #. f t a tasw e ' t

d tt r.. s .rrr r li .

21

Counting statistics play a major rule in than uncrtainty in the measure-ment ofV. This uncertainty appears in h unc rtinty in eterminnati n of(i.e., I/t). The unc trtainty due to ount g statietiks ms y be detrmined fromthe measured count distribution, us.in an vrror vstniator. Thy rlatbons ipgoverning the error estimator s*

4 V&r(*) usVar p ()t)

where p1 i the probability density.

It N the 4 total number of courts wda r the d4s1riboteI less any back -growd couns Is. var e the ndiidoat paranetrs n et the Ce tral-timIt

theorem griteriat (or no rv diesre o f . esmti otar m an .d ariawetthre rars.

Via" nast i the at t re$ II*a ip i IhaI the artIter thev r it w .S o.the ,re *w ts re4 r t o MA e 40a rae de mi r.With b 4, aMd are di w. Far st i heaw*er. i

de tr id prisrdy y the wity *4yirIhu*u j y st r staeri.dviriAs 4rwatti *. t wh are, the e t4 4i, tia i ti r dr* # a

San :4 ad therein r djet thur e * 4 the .qsse,*t

oi prfseavine 4w the py* I# .;rmmoat. the t 4srIi vi r C t6* wAdbvd wih the **4#i4*#. ta . q " the hot* heviet *w".h. ai r.

samy is aer dadtemnn t.TM e "- y i i aeatdta

the oiple retaM4whip

-er cA * e is l*er wh en..' *l4# end thr pry 6lioe ata a as tait 4vit v~ifL*Itd.

It 1* lviaueses M l* tAr. si tthv e aklri I44I4Mvirather I vi a vritrf' dCow srtl . Weier. ie twar.lMV 0 lv 1$ 64*m# aW# 44 I treAtId ** * i d+ te 1ttI d trrwr. rwr.

iiiw17tethe 4#4* 570 t m4 O rtrr

gI*AW

al

Up t thi p itr tht dt arc As*d to net (... bhave been removed prior t s lyoia)._Now w n w & h bits-*rowd nL4 art pru ent. First, wv ob trvv thal f w ti t ifrom the activated fl.iW is nerly *y*et i * id sen tud.,v. and the ba ckrrond ut i rate ont, ii vrwti s , dto kvdwill be o s than it tht diotr t.qtn is . ymmetrtt l" and tcnsnt rate *i* ip- pd

the average bhrkerawI sai ia h hant etra4

N .

* a # .n *t

rhe4'

W# thvee thne se k q 4d

the * ahre snal h t ane

T Th ern /ge the teriieeu s

4I *I b (# - #. ( eMs -*

Corwt4e eesa skewd * te oea*w #I *** em ews

00

V -

g #. , T te r 6 444 n4, 4 e a i vs - * N eh r ,Y c'4 M

I -

g /

-- -44 w- w #4m er ~ ~ rt~w

4 4~ 4 e?9(w s- $giePw 4pdren * egnMrga el e e'e 4 4 %

1. k 4ee#u4444 -r%9#4 +4be M- YAA 94e

q4etssw -4% (-e Mak 4e a9 &44-4 eey41+9*m

S$

.* #r44i# '.4 Mqrtw. Ae eed-st &.-$rr-w efwvw #4 he4#44 t 4 w r *- i qt. a e x'COY e# L *'c ".ree[ ., $4 .W . '- * . 1

-iO IPA-6 W M e -4 %M4s s- e & *4 4 0 er

y' + i.. e - .. de t sr e ap?..a w '" J" ,t ' -$ N 4 -g y .- ". #4

c 6 $ v wS ' t -. ;s x 9r ... " ii4i i -de4$ des.? ? 4 +g aage gy 4344 e sgew

ir.*I c . -Q L ?;+ r :m " .r 7 : ' C .. P" ! 4 y ; w C C: 8M#4.. w CJ e s t C +4 #9

!g s s*a #- Mm y160 v - * 0 0 0 T4 - M #9 4 agg r" '7 ^Y4 r

pp #7

vs #44 - W+f -«i9-#..,_ 4,i M Md; ~c - 1 p te* m i ai$

4% 9 #ik 44Iar*#>8- 4in #e444@* @ M 4g#14+m19( %'

(. rev, Po4i4-4.#mob+~- c,- p i.:4 d 4- - --

- + $ r. #- + g + :x!4 ;.-

11..,0 1i" .. -I _ «.!-% s

' 1 a!

4+ ' Iww ww 44+* aweesa4sg.%4wyi ~

A FieWM* $ +F' R+ 4-lie @ iV 4 l #4g - > t a !+V

AI

...

i v i of diL.

% aa'd.011.

t.w we** e %m d. p. s a * 0 as A(r. 6) aA constant.

f 4* 4

Sthw wferr *Ii4t stu #t y vIy ranm rime of .q aI tkiek.*A*a. 4I . a asd b. Let a ( b t ftRfr a11 cases; the. the ratio4m# # it b# en i o that trwm is

#aekw gebwe .141 # e fter bCR.

" . 1.6*...e,. e..th

as

t/.'4

A A

. "

_

41%l9 *

26

The above equation can be integrated with respect to r, observing that

b < R. to yield an estimate of the total gamma flux at p:

p= n[R/(R- r2 )] for r < R.

This relation is restricted for values of r < R because of its singularity prop-

erty at r = R.

The foregoing discussion has considered the various sources of error

in the PNA measurement. If we treat these errors as independent, normally

distributed errors, they can be combined to yield

fcV\ EL oz 1 Z 1 GB Z tz( = + - + + - - + - + EA + eD(43)

VL L N a Nc N 2Z D

where all terms have been previously defined except CA and CD, the respective

fractional uncertainties introduced in the measurement due to asymmetry of

the aci' ti arid detection processes. All the uncertainties except CA and eDcan be determined explicitly from the measured data. We can determine

CA and eD from computer simulation or estimate them from bounds determined

by analytic computations.

27

III. EXPERIMENT DESCRIPTION

A. Equipment

1. Instrumentation

The instrumentation used for the experiment consisted of a gamma-

detection system, a multiscaler, a pulsed neutron source, and a timing system.

A block diagram of the instrumentation system is shown in Fig. 3.

GAMMA NEUTRON

DETECTOR GENERATOR

LINEAR AMPPRE-AMP 4110- WITH MULTISCALER RMPS' LVPS"

DISCRI1MINA TOR

MYPS' INITIATE 1U~r

HIGH-VOLTAGE POWER SUPPLY

LOW-VOLTAGE POWER SUPPLY

Fig. 3. Block Diagram of PNA Instru roentation.

A N . Neg. No. 103-V5740.

The gamma-detection

system consisted of a Harshaw

127 x 127-mm NaI(TI) crystalwith an integral photomulti-plier, a Tennelec Model TC-133pulse preamplifier, and anOrtec Model 410 linear pulseamplifier. High voltage for

the photomultiplier was pro-

Model 2K-10 high-voltagepower supply.

The multiscaler usedwas a Technical Measurements

Corporation Model CN-1024 computer with a Model 214 multiscaler plug-inmodule. The Model 214 module provides upper- and lower-level discriminators

for rejection of unwanted gamma rays.

The pulsed neutron generator, a Sandia Model TC-655, requires

two power supplies. The high voltage was provided by a Power Designs

Model 2K-10 supply, and the low voltage by a Lambda Model LP-532-FMsupply.

Timing for the entire instrumentation system was provided by

two pulse generators. A Hewlett-Packard Model 8011A pulse generator wasoperated in the single-pulse manual mode and provided a negative pulse toinitiate the multiscaler operation. The same negative pulse w 'ted totrigger a Datapulse Model 110-B pulse generator, which provide -- ositivepulse to trigger the pulsed neutron generator. This timing circuit

repetitive pulsing of the system so that a number of pulses could be u'a selected flow level to improve the counting statistics for the measuremon...

2. Shielding

The shielding used for the work consisted of lead and 5 wt % borated

polyethylene. Design of the shielding for the neutron generator and gamma

detector included collimation as an integral part. 1the neutron genertorbeen used with a portable shield and a fixed shicl. The gamma dotrctorbeen used with only one shield. These shields are described below,

hashas

a. Port',le Shield and Neutron Collimator. The shield was de-signed to facilitate portability of the neutron source. it conistd of ii mmoflead with a ?6mm-dia cnllimation port in front of the neutron-generatin*surface: which was a 76"mm-dia disk source. The sides were I msm of lead,and the back was open. Figure 4 shows the dim nsions of the shield. Figure iis a photograph of the portable shield.

b. Fixed Shield and Neutron Collimator. The fixed shield wasdesigned to facilitate accuracy at the expc. se of poru.bility. This shield eon-sisted of 51 mm of load with a l6mmdia beam port in front of the neutronsource. The sides and back of the neutron generator were surrounded by102 mm of lead. This side and urik shielding was surrounded by SOS mm of5 wt % borated polyethylene. Figure 6 (left) shows the dimensions of the seld.Figure 7 is a photograph of the neutron shield mounted #4nst 4the secondary-sodium pipe. with the neutron generator t moved.

i

we'- 5th. A 1 a

1141 4 e# ,, w *Kn~wti r~flnnuem. MCI

1. ShIelding and roltimation forGnnma flete& tar

Shlvlding and rfllinatin for th

tamma tkiecior rensisir t 1$ mm of leadwith a l40m n-dia port $#t front of the Nalit)cr ystal4 Surroauniding the sides and ach of thedotauor wore 104 mm of lead. 1rw enflr. as.sumbly was mounted on a wheeled daily. rlg -ure (rIght) is a drawing A 4w shield andceltinmawr. Figure * is a pbangraph .1 theshIwl-andolly .sswnbly. Thur ;Mrmnnte ,,showa, is used O rni*or mh. temperature atthe detector.

1. ($.ntet rj

The system used M0r sh. np1011 can4isted 4 l - .s Q.a, n.min.l) pt4asn~il steel pipe, with a 9t .thw cennete s.

the t t.1 nlinary water stmpply. the Maten*gaerater, in the pwrtabl. shield. an the gammadetector were placed ahout nqua$ diswanwes fromthe elbow. Spcling between th. %en raint addeter alesg the mena renlins at the pip.was ;64 2 0.QI s m. The pipe was &P..4 mmin Q() and had a E~i1 -mm *41t.

28

I -

V

Am

inflmman.mmin.mminmin

- 14 2; .a t'4w - , ''..'

1 -*' I s'win. tec ,al:la

4 +

+ x x

3?A'

FUr*f :4 ;-,4 +411 I', . I$ 4.

xxw -,:. -nw. . ..

x x

!x Y. :W t ...

4.i, 'ia : . . [..1 2'; . V.. ', , I'?

+

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011N

vqupk

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:{

;r

Y.

Y

I

n.: :.r,

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t

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.r

Sf

-J : .: s? :.r 4c': c r. a '. , .

~l, fla#tO r$ #r Wa. 464 * 44.4

i

r*

I

r~ * "

". ) \.. _ ts ## -$ #* U wr4# t

414 4 4IK*r4;Ia n0 4 4 *9 ## * 4#4 14Otoo W 0,44

VW11 *0 9I 44 44 . 40- 4. rm*. W_

44 tow I t

Y #e7IF ## # wM # # # # e 4 !' Ma r4 A e

... 1.

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-WW wet %WM4. * 4 $##ew4uMWEM Mm t civil 'e

Men@# #9%+#~~41.Te#*fw4*r~ #senie49* e # MA4emeietwit Me## a4 fi*b"'' w4 ''#enet** ; .:. #44* i # '''wi

es~~~~~- 7h esiw % M 4

IkEAL 1f FS, i .: e$= =1-.r-te a T:.3

r a ' l Eau.t~

ROL st i ;4 4 &vs d .7 '. . l.

* -eneaan e

, pi }**,Rn ,M

4-a ..w.4

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wx. .--.. -2 C-f' : . . . . . .

'+"^ I 7_ I t ! w 'r ::"j s. '-.. d- l ' r ""3 ,w1 .. ;. "" .} .. t M' s ..- ... :" 1.A- --, z-- --- ---

."1. tia. ns .s ir: = .' d ' ;. ' t'_i .. f-# lr '...'1 (r.c.'t ., s. . l r :r' t : 3 . . w2 T:.i s . . *. :.r' 's Sx I. ;-:- - - - - -

:.-~n .ru ~ -'1? 2. ,: - -t. ::i 74 1 t -. 4r -. ss .n , - ..

yA t ptMi1: t

*.4.*

POP.: i(' t..

- -; e -

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I-

:'It

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If.. .

;J.;i . & .*4 .h i t +0' ' ts1 +:..:, u. :J3" Li.:;tgtr 1: - -. '

,j"r .. 1 i&:.Ci '. n« ?tlflJ . .. IY 4'2. .' +-. + i i i ! ++i:.J:i :

!.

- ..'

C

t \l"N.tILI J "

Ii 1 ,

1 Y

**1

r -x

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I

4 -- r

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fffli K

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w%'*A" i v t

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T -. - W- i400 4w u__ *40o.

-s4.e~ Me 1e ww; egr se &4e rwsqr# t *44#;*

swa k * s fl. ? %4****q~ M6e* * M~ 4 %9%.

t-ivo Wee aeMm S i4. 44 4qr aska Wes 4w* ### @ MIN # w.

4mmag #se4nw lannwsem a a~ 4 a *

/4&@@re4Ms# (ei WW 4w4 # |e44-~se -e fe 4..#e

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Wh ~ 4 V*-1 W### iie4% * be$a an es ewes

i $ .... . 4 *44 # duw i.v 44 . . t. *Awrai*x.

I-, wg 11(4- I r * JqI r

ge.

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+ * asg~sueag.* vp a#4, emws 4 e

$11s agr., easgeme pa~m sle ip a edi gaset4 etnes Nese lote

WA liwoe ef44%m

4 r 4i44y-s e - .i

";r , *&.a m r e p; KC_ 6', 3-I*;yJ . , - . . Ze. 4 -.5

s i ',4 'aE&a , tA?.'i~LuI uz

due.sE3. y eke 3y dss-A..G A $ -S 4+ * .orm

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^ Mt :

..- :. ,: 1 i 7. 'm ::." .. ": ' -I+ e . \ ., ' 'w d I :n .r .'1 :. : . ... ) rat.1:: . ?'. . e p;

C':-+ N' .' .# .. rw ; ; c- .+4 ' . 3- 4 $8 e" 044 s"'1

: t E * ' ov, 7 * -4 git 4 ,e asy *iRh4.a 4 I? . i 454 4 ~ J. 4'

- .$1.Fr$ .4 * p:-rel -:

' ,! ,.4 ! rg- , 4? ,- erk. 4-re ,u '. +- . ge e, .1i 4 -';+ *

;: ( rc "d . y 1'q: -. : ; "Li" 4(- 4 99 _id k l s e C ; S' e

. t r i "rr6 S k e s 04 +# i 4 44 8 > 'c f 4 .. 4 4 y 1 T

) #* * :zpjmk -

4 ii

- 8 :- ~~ 4 ~ 4 ~

" '! !. .+ - ... 1.w T w eedks . .. t e a pa a t..o..

r- i MMr 1.. #gr. ,,,,4t ? -, * - t @ r 'A . ;f

siig rk. . *

*O- yo 00, 4~~9*

4~~W *0ag0gg

:~i jig , l C , eggsM-4...bid +M r !mi l wau N A faI"iypl e 99f u . tl:rte i:"; ifj g ##g twenleg 9.i

i i ing ry p wag gg"i '' i p".r !W.IP4!, ."1:,.~.,fy: "'d

39

ci a ms qr 44

W $ cali

^s I 7 *S.1i )& _ 4rd 4 ,kk r 1 iw des

- - I .il- - - -4uu A :zf W-ez ~~L KSj~~ 444t8 ; 4e 4 1i dB - ew ' s

:)4 1V I:1 m i * s m096 16 t*I I49 4:1 11 4 i h o

n.* 1 T 4; w srn ~M flonww e ta~ t*~ ~ ~ at thtIowa lw vl

, a.lt. f x 4 5 4 4.1 :4I: WM t # w' p4 a gaies aA

i .> pwe"4 do. : et .atewavS. Ld~rm yt4Is. bas. enthe

v rd~prJ *t i*V P * wow44reth w d *u fle

l 440, st f. .. *somme ieawltesqw yisd to Vstahl ish a flow

0 fs. e w V r r asntrpr vd* tow O wins ation A ti rt which thc

4i # r ,e**Matr :. T .44 1 rom t ow fl t ris them

asped e aenwit tht fomthe h tor I mmt r at the 06 (ow level;

1010 wss etar ewdr i poer patoperation to 46%. Afterwasbaes a p ues te Weendry -" i ystvo i* . eon the

r r -- -m ... = -.-..- irirw~:r:-~..rrr : - - n M1I. ~

ti4)1 1i)

-emnm r -r . ~ ~ gwm ae e .:.m =an.

o.et

Iwo i r r, + C& O" "**" n tow leN veo t01 10. 0. 40 60.80.* K.. o fE4 . T O ab* the reared flow level, the operator

fmot t w4* fw te CM ftwreu. f;e* there should be a close agree-Oee ew 0a1 0. and tht flow Iwdtat.d by EM townRet r signal..

40

The agreement between these two ( O.?% difference) is indeed very good,showing that the operator did an excellent job in establishing and maintaining

flow levels. While the operator maintained the flow at a given level, the

voltage data were read from the EM and Foster flowmeters, and the PNAmeasurement was made.

The data tabulated in Table II are collated according to a preplannedtest sequence based on the nominal flow level at the measurement point.Figure 17 shows a typical count history for the secondary-flow measurement.The count histories for the measurement at each flow level are tabulated inAppendix A as Tables A.3-A.9.

1000.

100.

I0.

I.

0. 50. 100 . 150.

CHANNEL NO.200. 250. 300. 350.

Fig. 17. Count History for Measurement of Secondary-sodium Flow with Flow Levelat Nominal 901/o of Full Flow. ANL Neg. No. 103-U5451.

Table III displays the data from Table II, but converted to units of flow.These data are correlated further with the PNA data in the next section ofthis report.

* 5-MS CHANNEL WIDTHS

*.1.

S""

".." *, "

we 0. . . .. . . . . ..0

"e. " ". " " " ..". "" ," "0. " " 0" "9 M . " " " . M .04

" " 00" 0 " 0 " 00 0 00 m

" " 0"". "@ .* "

41

TABLE l. Secondary-system Volumwtrp e7w ac-pte .r 477u th $ d

as MteasuredI by thw E.M and 1Fostter Elr-me-terR

Nominal Secondary- Flow tat. mb.system Flow Level. .. grner fur

% EM Flowmtera Foster Flow;mwterb Otaput

0 0.0 0.0 0.010 0.0382 0.0395 1.07LO 0.0752 0.0759 1,O240 0.1497 0.1457 0.95060 0.253 0.2189 0.7E480 0.3009 0.2982 1.029490 0.3376 0.3397 1.01795 0.3565 ().%606 0.954

aDetermined from: Flow = 0.006765 x millivolts from Table It.bDetcrmined from: Flow = 0.2890 voltage of Table 11.CSum of output-monitor indications divided by total number of pulsee normralttat

to the average level of 5.091 per pulse.dVoltage on neutron generat--r increased at this point for the rest of the test.

V. DATA ANALYSIS

A. Mockup Test

The mockup test was directed primarily toward checkout of the equip.ment. Consequently, only a limited amount of data was acqired on the waterflow rates in this test.

Table A.1 of Appendix A contains the Irultiscaler data obtained frontthe test. These data were analyzed in accordance with Eq. ZI after a constantvalue for background had been removed from the raw data. The uncertaintyin the measurement was estimated using Eq. 43, with the asymmetry uncer-tainties taken as zero and the spatial dispersion of activated nuclei, o. taken

as twice the diameter of the beam port.

An exhaustive analysis of the data was not justified because of thelarge measurement uncertainty (~ 5%) of the totalizing flowmeter (totalier),Table IV presents the results of the analysis of data from the mockup test.As can be seen, there is reasonably good agreement between the flow rate-measured with the pulsed-neutron technique and those measured with thetotalizer. The totalizer is of the. type used in culinary water supplies. Itserror is typically flow-rate-dependent and decreases with increasing flow rate.

TABLE IV. Flow VdQlities in Mockup Test

Totaliz .r l:;A

Water Flow Flow VelocityTest Temp. Velocity. Urscertainty. Velocity. Uncertainty. Comparison.No. F( C) m/s mci/s PNA/Totaliltr

1 60(16) 0.610 5 0.579 1.4 0.952 60(16) 0.914 5 0.887 1.4 0.97

42

This rg wririied by t ckei#:# th mi l re r* Ar -s xuNaor '0. *milerm@ tar, T~ho vacuy o1 this typ of sotolat ctt-i ii +rgeir O ewit tss

rawe within it p rating, r rwi . CM a uetly. f1 taav1 wt v es

by PNA .pp ars to iiw mitre **r rfsi tk it$. ._1 CAMAW thV- agVr V et I twren th*- t impors -:: t iai on r A ed#e- wiy.

I. #*n y. #1w reht v *om th *dmii 1%-S lt+ wiapplicat i o+ th A eekiq r4* w4td 4ao r i

o. Da tor -d v Flow

Ao Thv -w 1tr #-#. 116, o. it rot s ski t r ,1w *t.

count* i the h.m*i he ter -1tt 1 Zia i4s e 1toy- '. 1#Wa s rV4 a

r. et 0 LESQ t 1i i t i 1 1r

dt: m *o*ad t . I E 11=r .. 'h i o-4* 4 ' t t.dutyeatt costa i 1t b,1rutera iwent argewe set t hw

*ma i d pe4 -4rprs#iw T *'* s f* d - rt pen t 1 1wr *r#w a osn w

dt* h v@ire t * W v * 1 1. Ow- A VOW -. 4w v- tthuton e rt atewna h rhuw e e A nsaaa

bre aouceacy at in 11w epr ti**ikd t sa te~a paap p

As o U irth dlp itse w 0 4*d4it 4 t4 . *i # w$ t is rv1s t W- I lw1. s 0 w iervm 4 d f o 4t'0 **w 7% uievnwe rr# t wret -

t rm ha rmie v oftmi tatii a t romte4mat hn* aapdt t

0 to && ol l . 0 * w rv statedtoo 0eqas t+ f swtrm

tia 1 eat -qur 1i fi grotee.*

Svveiroldit1*ren iris ifor Ls owr w V'at w4. Tewr 1a ietyte

#()a A$ exp .01M

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TABLE A.3. Count History for PNA Measurement of Sodium Flow:Nominal Flow Level 10%, Multiscaler Channel Width 50 ms

(1- (51- (101- (151- (201- (251- (301- (351- (401- (451-Channels 50) 100) 150) 200) 250) 300) 350) 400) 450) 500)

14 4 19 7 2 1 5 Q2 3 28 15 3 3 2 0 0 05 5 21 13 3 1 1 0 0 03 4 26 12 2 1 2 0 0 00 4 21 8 2 2 1 0 0 00 1 22 13 1 2 0 0 0 02 4 22 6 o 4 0 0 0 02 2 23 4 4 2 0 0 0 02 3 34 7 2 1 0 0 0 02 1 34 10 3 4 0 0 0 02 3 31 8 2 6 0 0 0 05 4 42 4 7 1 0 0 0 02 2 48 8 2 1 0 0 0 02 1 31 6 1 4 0 0 0 03 1 34 6 4 6 0 0 0 03 3 48 10 1 3 0 0 0 01 3 38 7 0 5 0 0 0 02 2 29 6 5 3 0 0 0 02 4 42 9 1 3 0 0 0 03 0 39 3 2 3 0 0 0 00 3 40 3 3 2 0 0 0 02 1 35 2 1 2 0 0 0 02 3 38 4 3 2 0 0 0 02 3 52 7 2 0 0 0 0 04" 0 35 4 3 1 0 0 0 04 5 51 2 3 2 0 0 0 01 1 40 1 4 1 0 0 0 03 1 40 6 5 3 0 0 0 02 5 35 2 3 0 0 0 0 03 3 36 6 2 3 0 0 0 06 5 45 2 2 1 0 0 0 01 12 38 8 0 2 0 0 0 01 4 30 3 0 3 0 0 0 03 3 40 4 5 2 0 0 0 03 3 26 4 4 3 0 0 0 01 7 31 2 3 0 0 0 04 6 32 2 1 3 0 0 0 01 9 22 ! 0 1 0 0 0 01 5 28 4 1 3 0 0 0 00 9 22 1 2 4 0 0 0 02 8 19 4 5 0 0 0 0 03 3 22 1 1 2 0 0 0 04 8 27 0 4 4 0 0 0 01 7 19 1 4 2 0 0 0 02 11 16 3 3 2 0 0 0 04 15 19 4 0 3 0 0 0 02 19 19 5 3 3 0 0 0 04 11 16 6 2 0 0 0 0 03 17 15 4 1 4 0 0 0 02 13 16 4 0 3 0 0 0 0

55

TABLE A.4. Count History for PNA Measurement of Sodium Flow:Nominal Flow Level 20%, Multiscaler Channel Width 25 ms

(1- (51- (101- (151- (201- (251- (301- (351- (401- (451-Channels 50) 100) 150) 200) 250) 300) 350) 400) 450)I 5p

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11 13 53 27 15 16 5 13 10 1413 14 50 36 7 5 10 8 10 622 11 55 39 17 14 9 10 9 1211 12 60 33 12 7 15 10 4 7

10 4 71 31 10 S 7 11 7 15

17 12 70 24 12 15 11 13 12 718 7 81 i8 10 9 14 3 12 12

17 11 95 26 15 13 14 13 14 8

13 15 118 24 9 10 13 8 11 17

10 11 99 26 8 8 15 10 5 613 7 92 26 1 10 16 1 1 13 13

13 12 88 38 15 14 8 10 10 822 7 103 23 8 a 12 10 12 1219 16 111 27 12 13 9 12 S 7

10 14 116 lb 10 9 13 12 1/ 1516 10 105 22 14 11 13 13 15 912 13 101 17 12 9 16 13 11 1120 13 125 22 12 13 8 10 11 1016 15 120 11 6 9 b 12 9 a14 12 118 18 14 13 17 9 10 914 15 107 13 1b S 10 10 12 10

18 6 100 11 8 11 10 7 9 1215 17 115 15 11 16 10 14 6 1420 16 106 16 8 10 13 12 7 9

15 11 92 21 17 16 8 15 9 a18 11 93 lb 5 9 14 9 7 1610 16 88 11 12 14 11 9 13 8

9 15 90 8 5 7 15 5 8 920 15 81 14 12 11 7 8 13 714 12 82 17 7 10 13 12 8 717 15 101 12 10 15 9 13 8 11

12 21 80 10 9 9 7 9 8 1015 22 78 14 12 9 14 10 10 13

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7 31 48 17 8 6 10 12 13 119 29 57 22 12 5 12 10 10 79 30 48 14 13 12 10 12 13 b

13 35 37 11 10 6 13 15 10 1210 28 38 10 12 13 14 10 11 6

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